We present the results of a campaign of simultaneous X-ray and optical observations of true type 2 Seyfert galaxies candidates, i.e. active galactic nuclei without a broad-line region (BLR). Out of the initial sample composed of eight sources, one object, IC 1631, was found to be a misclassified starburst galaxy, another, Q2130-431, does show broad optical lines, while other two, IRAS 01428-0404 and NGC 4698, are very likely absorbed by Compton-thick gas along the line of sight. Therefore, these four sources are not unabsorbed Seyfert 2s as previously suggested in the literature. On the other hand, we confirm that NGC 3147, NGC 3660 and Q2131-427 belong to the class of true type 2 Seyfert galaxies, since they do not show any evidence for a broad component of the optical lines nor for obscuration in their X-ray spectra. These three sources have low accretion rates (m?=L bol /L Edd ?0.01), in agreement with theoretical models which predict that the BLR disappears below a critical value of Lbol/LEdd. The last source, Mrk 273x, would represent an exception even of these accretion-dependent versions of the Unification Models, due to its high X-ray luminosity and accretion rate, and no evidence for obscuration. However, its optical classification as a Seyfert 2 is only based on the absence of a broad component of H beta, due to the lack of optical spectra encompassing the Ha band.